2,938 research outputs found
Scale Invariant Cosmology
An attempt is made here to extend to the microscopic domain the scale
invariant character of gravitation - which amounts to consider expansion as
applying to any physical scale. Surprisingly, this hypothesis does not prevent
the redshift from being obtained. It leads to strong restrictions concerning
the choice between the presently available cosmological models and to new
considerations about the notion of time. Moreover, there is no horizon problem
and resorting to inflation is not necessary.Comment: TeX, 20 page
I - Matter, antimatter and geometry II - The twin universe model : a solution to the problem of negative energy particles III - The twin universe model plus electric charges and matter-antimatter symmetry
We introduce a new dynamical group whose coadjoint action on its momentum
space takes account of matter-antimatter symmetry on pure geometrical grounds.
According to this description the energy and the spin are unchanged under
matter-antimatter symmetry. We recall that the antichron components of the
Poincar\'{e} group, ruling relativistic motions of a mass-point particle,
generate negative energy particles. The model with two twin universes, inspired
by Sakharov's one, solves the stability issue. Positive and negative energy
particles motions hold in two distinct folds. The model is extended to charged
particles. As a result, the matter-antimatter duality holds in both universes.Comment: 19 Fevrier 200
On the quaternion -isogeny path problem
Let \cO be a maximal order in a definite quaternion algebra over
of prime discriminant , and a small prime. We describe a
probabilistic algorithm, which for a given left -ideal, computes a
representative in its left ideal class of -power norm. In practice the
algorithm is efficient, and subject to heuristics on expected distributions of
primes, runs in expected polynomial time. This breaks the underlying problem
for a quaternion analog of the Charles-Goren-Lauter hash function, and has
security implications for the original CGL construction in terms of
supersingular elliptic curves.Comment: To appear in the LMS Journal of Computation and Mathematics, as a
special issue for ANTS (Algorithmic Number Theory Symposium) conferenc
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